Question

For the graph to the right, describe the composition of transformations that maps ΔHPW to ΔΝΑΤ.Which composition of transformations below maps ΔHPW to ΔNAT? Select the correctchoice below and fill in the answer boxes to complete your choice.(Type an integer or a decimal.)

Answer 1

Step-by-step explanation:

First, we notice that ΔΝΑΤ is greater than ΔHPW, so there was a dilation, the factor of dilation can be calculated comparing the length of corresponding sides of the triangles. So, if we compare NT with HW, we get:

`(NT)/(HW)=(3)/(2)=1.5`

Therefore, the first transformation was a dilation by a factor of 1.5.

So, with this transformation, the coordinates of the original triangle will be equal to:

(x, y) ----------> (1.5x, 1.5y)

H(-6, -4) -----> (1.5(-6), 1.5(-4)) = (-9, -6)

P(2, -6) ------> (1.5(2), 1.5(-6)) = (3, -9)

W(-6, -6) ----> (1.5(-6), 1.5(-6)) = (-9, -9)

Then, the transformation is a rotation of 180° about the origin because the rule that these coordinates follow are:

(x, y) ------> ( -x, -y)

(-9, -6) ----> N(9, 6)

(3, -9) ------> A(-3, 9)

(-9, -9) -----> T(9, 9)

Therefore, the answer is:

C. D1.5 a